Energy continued translational

The SRP and SRP receptor then mediate insertion of the nascent secretory protein into the translocon. Hydrolysis of GTP by the SRP and its receptor drive this docking process (see Figure 16-6). As the ribosome attached to the translocon continues translation, the unfolded protein chain is extruded into the ER lumen. No additional energy is required for translocation. 

The differential cross-section defined by (B.6.1) is related to the state-resolved differential cross-section as follows. First we go over from discrete final internal state indices to a continuous translational energy variable... 

Translation of a quantum mechanical particle in a container corresponds to a bound state with the energy quantized. Translation of a particle, such as an atom or molecule, in an unrestricted space (no walls and no potentials) is an unbound motion. The mechanics of such a free particle have certain similar elements in both the quantum and classical pictures. In both, the energy may vary continuously. In chemistry then, energy storage depends on the nature of the mechanical system and on whether or not there are bound states. We will revisit all of the quantum mechanical systems discussed earlier later in the book. 

When the two objects come into contact with each other, molecules in the hotter object give up some of their kinetic energy through collisions with molecules in the colder object. The transfer of energy continues until the average kinetic energies of the molecules in the two objects become equal, that is, until the temperatures equalize. Finally, the idea expressed in equation (6.21) provides a new way of looking at the absolute zero of temperature It is the temperature at which translational molecular motion should cease. 

Translational energy, which may be directly calculated from the classical kinetic theory of gases since the spacings of these quantized energy levels are so small as to be negligible. The Maxwell-Boltzmann disuibution for die kinetic energies of molecules in a gas, which is based on die assumption diat die velocity specuum is continuous is, in differential form. 

We recall, from elementary classical mechanics, that symmetry properties of the Lagrangian (or Hamiltonian) generally imply the existence of conserved quantities. If the Lagrangian is invariant under time displacement, for example, then the energy is conserved similarly, translation invariance implies momentum conservation. More generally, Noether s Theorem states that for each continuous N-dimensional group of transformations that commutes with the dynamics, there exist N conserved quantities. 

If, now, we continue warming the substance sufficiently, we will reach a point at which the kinetic energies in vibration, rotation, and translation become comparable to chemical bond energies. Then molecules begin to disintegrate. This is the reason that only the very simplest molecules—diatomic molecules—are found in the Sun. There the temperature is so high (6000°K at the surface) that more complex molecules cannot survive. 

The behaviour of electrons in metals shows the translational properties of quantum particles having quantized energy levels. These cannot be approximated to the continuous distribution describing particles in a gas because of the much smaller mass of the electron when compared with atoms. If one gram-atom of a metal is contained in a cube of length L, the valence electrons have quantum wavelengths, X, described by the de Broglie equation... 

Electronic levels are spaced more closely together at higher quantum numbers as the ionization limit is approached, vibrational levels are evenly spaced, while rotational and translational levels are spaced further apart at high energies. The classical principle assumes continuous variation of all energies. 

The result (Equation 4.90) could have been derived more simply. It has been emphasized that the quantum mechanical contribution to the partition function ratio arises from the quantization of vibrational energy levels. For the molecular translations and rotations quantization has been ignored because the spacing of translational and rotational energy levels is so close as to be essentially continuous (As/kT 1). 

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